I have not been able to come up with a way to overcome p!=np
in logic, so I am thinking about developing a heavily typed logic (logic-like
references) as a way to get around the bottleneck of exponential complexity.
However, I have run into some difficulties there as well.


I would like an object (a concept or a concept fragment) to
be able to inherit from different type categories.


The categorical types would be familial categories meaning
that every object (of that type) possessed some features of the type family but
they would not necessarily possess all the features of the family.


Subtypes (composed of collections of objects) would be used to
better represent the type hierarchies. Relations between objects or between
types would be treated as conceptual objects themselves.


The fluidity of this kind of typing would make the system
more natural than old AI but it would be much more difficult to program. I 
initially
want to use this system as a way of cross-indexing a text document that a user
could set up. It is my hope that I would be able to develop an AI system that
would be capable of learning to read – to some extent – based on the conceptual
relations that the user taught it (and continued to teach it).


One idea that I had is that I might use non-familial
categorical types right at the level above the conceptual objects. The objects
of the non-familial category type would inherit (or possess) all the features
of the type. Then if a set of features were triggered in an individual (concept
object) the sub-family types might be identified and in a reverse manner, if
the sub-family typing were pointedly used as representations of features then a
better assessment of the conceptual objects that possessed those features (or
of the type of objects that would possess those objects) could be made. This
would be useful in learned references.


I am thinking about working on an easily feasible program
that would actually be useful. Then once I got into it I might be able to
develop the idea to give it a genuine AI feature. I think text based search
engine look-up has actually deteriorated a little during the past 10 years.
I just looked up familial categories and my first reference was 
https://en.wikipedia.org/wiki/Category:Family . Going with categorical family I 
came up with https://en.wikipedia.org/wiki/Categorical_distribution and 
https://plato.stanford.edu/entries/category-theory , none of which are actually 
related to what I am talking about. I finally
put, “categorical family Wittgenstein” and I found one reference on Stack
Exchange that looks like it might be a little relevant. 
https://philosophy.stackexchange.com/questions/40581/on-wittgensteins-family-resemblance-and-machine-learning



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